In a large skillet, add the olive oil and ground turkey, sprinkle with the garlic powder, onion powder, paprika, salt and pepper and cook, breaking up with the back of a wooden spoon or potato masher, until the meat is no longer pink, about 5 minutes. Add the garlic, bell peppers and onions and season with salt and pepper. Cook until the vegetables soften, about 5 minutes.
Add the crushed tomatoes, tomato puree, ketchup, brown sugar, mustard, vinegar and Worcestershire sauce. Bring the mixture to a boil, reduce to a simmer and cook, stirring occasionally, until the sauce thickens up, 10 to 15 minutes. Serve warm on toasted potato rolls.